An improved positioning model of deep-seafloor datum point at large incidence angle

The inhomogeneous sound speed in seawater causes refraction of sound waves,and the elimination of the refraction effect is essential to the accuracy of underwater acoustic positioning.The raytracing method is an indispensable tool for effectively handling problems.However,this method has a conflict between localization accuracy and computational quantity.The equivalent sound speed profile(ESSP)method uses a simple sound speed profile(SSP)instead of the actual complex SSP,which can improve positioning precision but with residual error.The residual error is especially non-negligible in deep water and at large beam incidence angles.By analyzing the residual error of the ESSP method through a simulation,an empirical formula of error is presented.The data collected in the sailing circle mode(large incidence angle)of the South China Sea are used for verification.The experiments show that compared to the ESSP method,the improved algorithm has higher positioning precision and is more efficient than the ray-tracing method.

Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

An ERA5 tropospheric parameters-augmented approach for improving GNSS precise point positioning

Precise Point Positioning(PPP) technology has developed into a potent instrument for geodetic positioning, ionospheric modeling, tropospheric atmospheric parameter detection, and seismic monitoring.As atmospheric reanalysis data products’ accuracy and spatiotemporal resolution have improved recently, it has become important to apply these products to obtain high-accuracy tropospheric delay parameters, like zenith tropospheric delay(ZTD) and tropospheric horizontal gradient. These tropospheric delay parameters can be applied to PPP to reduce the convergence time and to increase the accuracy in the vertical direction of the position. The European Centre for Medium-Range Weather Forecasts Reanalysis 5(ERA5) atmospheric reanalysis data is the latest product with a high spatiotemporal resolution released by the European Center for Medium-Range Weather Forecasts(ECMWF). Only a few researches have evaluated the application of ERA5 data to Global Navigation Satellite System(GNSS)PPP. Therefore, this study compared and validated the ZTD products derived from ERA5 data using ZTD values provided by 290 global International GNSS Service(IGS) stations for 2016-2017. The results indicated a stable performance for ZTD, with annual average bias and RMS values of 0.23 cm and 1.09 cm,respectively. Further, GNSS observations for one week in each of the four seasons(spring: DOY 92-98;summer: DOY 199-205;autumn: DOY 275-281;and winter: DOY 22-28) from 34 multi-GNSS experiments(MGEX) stations distributed globally in 2016 were considered to evaluate the performance of ERA5-derived tropospheric delay products in GNSS PPP. The performance of ERA5-enhanced PPP was compared with that of the two standard GNSS PPP schemes(without estimated tropospheric horizontal gradient and with estimated tropospheric horizontal gradient). The results demonstrated that ERA5-enhanced GNSS PPP showed no significant improvement in the convergence times in both the Eastern(E) and Northern(N) directions, while the average convergence time over four weeks in the vertical(U)direction improved by 53.3% and 52.7%, respectively(in the case of pngm station). The average convergence times for each week in the U direction of the northern and southern hemisphere stations indicated a decrease of 16.3%, 12.6%, 9.6%, and 9.1%, and 16.9%, 9.6%, 8.9%, and 14.5%, respectively.Regarding positioning accuracy, ERA5-enhanced PPP showed an improvement of 13.3% and 16.2% over the two standard PPP schemes in the U direction, respectively. No significant improvement in the positioning performance was observed in both the E and N directions. Thus, this study demonstrated the potential application of the ERA5 tropospheric parameters-augmented approach to Beidou navigation and positioning.

Deformation caused by the 2011 eastern Japan great earthquake monitored using the GPS single-epoch precise point positioning technique

Crustal deformation can provide constraints for studying earthquake rupture and shock wave transmission for the Mw9.0 eastern Japan great earthquake. Using the single- epoch precise point positioning （PPP） method and the appropriate positioning flow, we process GPS data from six IGS （International GNSS Service） sites （e.g., MIZU, TSK2, USUD, MTKA, AIRA and KSMV） located in Japan and obtain the positioning results with centimeter scale precision. The displacement time series of the six sites are analyzed using the least squares spectral analysis method to estimate deformations caused by the Mw9.0 mainshock and the Mw7.9 aftershock, and the cumulative displacements after 1 day. Mainshock displacements at station MIZU, the nearest site to the mainshock in the North （N）, East （E）, and Up （U） directions, are -1.202 m, 2.180 m and -0.104 m, respectively, and the cumulative deformations after 1 day are -1.117 m, 2.071 m and -0.072 m, respectively. The displacements at station KSMV, the nearest site to the Mw7.9 aftershock in the N, E and U directions, are -0.032 m, 0.742 m and -0.345 m, respectively. The other sites obviously experienced eastern movements and subsidence. The deformation vectors indicate that the horizontal displacements caused by the earthquake point to the epicenter and rupture. Elastic bounds evidently took place at all sites. The results indicate that the crustal movements and earthquake were part of a megathrust caused by the Pacific Plate sinking under the North American Plate to the northeast of Japan island arc.

Modified algorithm of combined GPS/GLONASS precise point positioning for applications in open-pit mines

A modified algorithm of combined GPS/GLONASS precise point positioning （GG-PPP） was developed by decreasing the number of unknowns to be estimated so that accurate position solutions can be achieved in the case of less number of visible satellites. The system time difference between GPS and GLONASS （STDGG） and zenith tropospheric delay （ZTD） values were firstly estimated in an open sky condition using the traditional GG-PPP algorithm. Then, they were used as a priori known values in the modified algorithm instead of estimating them as unknowns. The proposed algorithm was tested using observations collected at BJFS station in a simulated open-pit mine environment. The results show that the position filter converges much faster to a stable value in all three coordinate components using the modified algorithm than using the traditional algorithm. The modified algorithm achieves higher positioning accuracy as well. The accuracy improvement in the horizontal direction and vertical direction reaches 69% and 95% at a satellite elevation mask angle of 50°, respectively.

Positioning performance analysis on combined GPS/BDS precise point positioning

Combining the observation data from five Multi-GNSS Experiment(MGEX)stations with the precise orbit and clock products from Global Positioning System(GPS)and BeiDou Navigation Satellite System(BDS),we studied the model of combined GPS/BDS precise point positioning,and then analyzed the convergence speed and short-time(6 h)positioning accuracy.The calculation results show that in static positioning,the average convergence time of GPS is about 50 min,and its horizontal accuracy is better than 2 cm while the vertical accuracy is better than 4 cm.The convergence speed of combined GPS/BDS is about 40 min,and its positioning accuracy is close to that of GPS.In kinematic positioning,the average convergence time of GPS is about 72 min,and its horizontal accuracy is better than 5 cm while the vertical accuracy is better than 12 cm.The average convergence time of GPS/BDS is about 57 min,and its horizontal accuracy is better than 3 cm while the vertical accuracy is better than 9 cm.Combined GPS/BDS has significantly improved the convergence speed,and its positioning accuracy is slightly than that of GPS.

Precise point positioning and its application in mining deformation monitoring

Precise point positioning (PPP)-based deformation monitoring scheme is presented for the use in mining deformation monitoring. Within the solutions of daily observation, outliers are detected and removed to avoid any potential misinterpretation of the results and then the deformation can be extracted by the coordinate differences between the two consecutive solutions. Meanwhile, because of the special location of a rover station in mining areas, the satellite geometry may be insufficient for a reasonable PPP solution, and the multipath impact an also be significant. Therefore, it is necessary to predict the satellite geometry before any daily observation. To evaluate the ability of extracting the deformation using the PPP-based method, various quality measures were introduced. The results of three datasets of the same station show that the precision of deformation monitored by PPP can reach up to cm level and even mm level.

Single Point Positioning with Sequential Least-Squares Filter and Estimated Real-Time Stochastic Model

To obtain higher accurate position estimates, the stochastic model is estimated by using residual of observations, hence, the stochastic model describes the noise and bias in measurements more realistically. By using GPS data and broadcast ephemeris, the numerical results indicating the accurate position estimates at sub-meter level are obtainable.

Single Point Positioning Using GPS, GLONASS and BeiDou Satellites

This paper introduces the Chinese BeiDou satellite system and its comparison with the actual completed American GPS and the Russian GLONASS systems. The actual BeiDou system consists of 14 satellites covering totally the Asia-Pacific area. A Single Point Positioning (SPP) test has been realised in Changsha, Hunan province, China, to show the advantage of using combined pseudorange solutions from these 3 satellite navigation systems especially in obstructed sites. The test shows that, with an elevation mask angle of 10°, the accuracy is improved by about 20% in horizontal coordinates and nearly 50% in the vertical component using the simultaneous observations of the 3 systems compared to the GPS/GLONASS solution. For the processing with an elevation mask angle of 30°, most of the time less than 4 GPS satellites were available for the GPS-only case and no solution was possible. However, in this difficult situation, the combined GPS/GLONASS/ BeiDou solutions provided an accuracy (rms values) of about 5 m.

Estimation of annual variation of water vapor in the Arctic Ocean between 80°–87°N using shipborne GPS data based on kinematic precise point positioning

The measurement of atmospheric water vapor （WV） content and variability is important for meteorological and climatological research. A technique for the remote sensing of atmospheric WV content using ground-based Global Positioning System （GPS） has become available, which can routinely achieve accuracies for integrated WV content of 1-2 kg/m2. Some experimental work has shown that the accuracy of WV measurements from a moving platform is comparable to that of （static） land-based receivers. Extending this technique into the marine environment on a moving platform would be greatly beneficial for many aspects of meteorological research, such as the calibration of satellite data, investigation of the air-sea interface, as well as forecasting and climatological studies. In this study, kinematic precise point positioning has been developed to investigate WV in the Arctic Ocean （80°-87°N） and annual variations are obtained for 2008 and 2012 that are identical to those related to the enhanced greenhouse effect.

Signal quality analysis and quality check of BDS3 Precise Point Positioning in the Arctic Ocean

This study analyzes the signal quality and the accuracy of BeiDou 3 rd generation Satellite Navigation System(BDS3) Precise Point Positioning(PPP) in the Arctic Ocean. Assessment of signal quality of BDS3 includes signal to noise ratio(SNR), multipath(MP), dilution of precision(DOP), and code-minus-carrier combination(CC). The results show that, 5 to 13 satellites are visible at any time in the Arctic Ocean area as of September 2018, which are sufficient for positioning. In the mid-latitude oceanic region and in the Arctic Ocean, the SNR is 25–52 dB Hz and the MP ranges from-2 m to 2 m. As the latitude increases, the DOP values show large variation, which may be related to the distribution of BDS satellites. The CC values of signals B1 I and BIC range from-5 m to 5 m in the mid-latitude sea area and the Arctic Ocean, which means the effect of pseudorange noise is small. Moreover, as to obtain the external precise reference value for GNSS positioning in the Arctic Ocean region is difficult, it is hard to evaluate the accuracy of positioning results. An improved isotropy-based protection level method based on Receiver Autonomous Integrity Monitoring is proposed in the paper, which adopts median filter to smooth the gross errors to assess the precision and reliability of PPP in the Arctic Ocean. At first, the improved algorithm is verified with the data from the International GNSS Service Station Tixi. Then the accuracy of BDS3 PPP in the Arctic Ocean is calculated based on the improved algorithm. Which shows that the kinematic accuracy of PPP can reach the decimeter level in both the horizontal and vertical directions, and it meets the precision requirements of maritime navigation.

Comparison of availability and reliability among different combined-GNSS/RNSS precise point positioning

With emergence of the BeiDou Navigation Satellite System(BDS), the Galileo Satellite Navigation System(Galileo), the Quasi-Zenith Satellite System(QZSS)and the restoration of the Global Navigation Satellite System(GLONASS), the single Global Positioning System(GPS) has been gradually expanded into multiple global and regional navigation satellite systems(multi-GNSS/RNSS). In view of differences in these 5 systems, a consolidated multi-GNSS/RNSS precise point positioning(PPP) observation model is deduced in this contribution. In addition, the performance evaluation of PPP for multi-GNSS/RNSS is conducted using a large number of the multi-GNSS experiment(MGEX) station datasets. Experimental results show that multi-GNSS/RNSS can guarantee plenty of visible satellites effectively. Compared with single-system GPS, PDOP, HDOP, and VDOP values of the multi-GNSS/RNSS are improved by 46.8%, 46.5% and 46.3%, respectively. As for convergence time, the static and kinematic PPP of multi-GNSS/RNSS are superior to that of the single-system GPS, whose reliability, availability, and stability drop sharply with the increasing elevation cutoff. At satellite elevation cutoff of 40 °, the single-system GPS fails to carry out continuous positioning because of the insufficient visible satellites, while the multi-GNSS/RNSS PPP can still get positioning solutions with relatively high accuracy, especially in the horizontal direction.

Semi-parametric Adjustment Model Methods for Positioning of Seafloor Control Point

This paper focus on solving the problem of seafloor control point absolute positioning with low vertical accuracy based on the survey ship sailing circle. The method of dealing with the systematic error based on a semi-parametric adjustment model was proposed. Firstly, the influence of sound velocity change on ranging error is analyzed. Secondly, a semi-parametric adjustment model for determining three-dimensional coordinates of seafloor control points was established. And respectively proposed solutions under two different conditions, the observation duration is an integral multiple or non-integer multiple of the long-period term of the ranging error. The simulation experiment shows that this method can obviously improve the accuracy of vertical solution of seafloor control point compared with the difference technique and the least-squares method when internal waves exist and observation duration is less than an integer multiple of the long-period term of the ranging error.

Impact of Tropospheric Delay Gradients on Total Tropospheric Delay and Precise Point Positioning

GPS signals are electromagnetic waves that are affected by the Earth’s atmosphere. The Earth’s atmosphere can be categorized, according to its effect on GPS signals, into the ionosphere (ionospheric delay) and neutral atmosphere (tropospheric delay). The first-order ionospheric delay can be eliminated by linear combination of GPS observables on different frequencies. However, tropospheric delay cannot be eliminated because it is frequency-independent. The total tropospheric delay can be divided into three components. The first is the dry component, the second part is the wet component, and the third part is the horizontal gradients which account for the azimuthal dependence of tropospheric delay. In this paper, the effect of modeling tropospheric gradients on the estimation of the total tropospheric delay and station position is investigated. Long session, one month during January 2015, of GPS data is collected from ten randomly selected globally distributed IGS stations. Two cases are studied: the first case, the coordinates of stations are kept fixed to their actual values and the tropospheric delay is estimated twice, with and without tropospheric gradients. In the second case, the station position is estimated along with the total tropospheric delay with and without tropospheric gradients. It is shown that the average bias of the estimated total tropospheric delay when neglecting tropospheric gradients ranges from ?1.72 mm to 2.14 mm while the average bias when estimating gradients are ?0.898 mm to 1.92 mm which means that the bias is reduced by about 30%. In addition, the average standard deviation of the bias is 4.26 mm compared with 4.52 mm which means that the standard deviation is improved by about 6%.

Application of precise point positioning technology in airborne gravity measurement

The precise point positioning （PPP） technology is applied to an airborne gravity survey. By analyzing the advantages and disadvantages of several velocity and acceleration measurement methods and in combination with an actual marine gravity survey, the position difference method is confirmed to be a useful survey method for velocity and acceleration. Finally, the practicability of using PPP in airborne marine gravity survey is verified by measured data.

Endemic error correction model and quantitative analysis of precise point positioning

To identify the endemic error of the precise point positioning which cannot be weakened or eliminated in precise point positioning (PPP) zero-difference model, the 24 h observation data acquired from CHAN station on Oct 31st, 2010, were adopted for analyses, different correction models of various errors were discussed and their influences on traditional zero-difference model were analyzed. The results show that the errors cannot be ignored. They must be corrected with suitable models and estimated with auxiliary parameters. The influence magnitudes of all errors are defined, and the results have guiding significance to improve the accuracy of precise point positioning zero-difference model.

Performance analysis of real-time and post-mission kinematic precise point positioning in marine environments

This article focuses on the performance analysis of both real-time and post-mission kinematic precise point positioning(PPP)in challenging marine environments.For this purpose,a real dynamic experiment lasting 6 h was carried out on a lake dam in?orum City of Turkey.While the kinematic test was continuing,the real-time PPP coordinates were obtained for each measurement epoch with a commercial real-time PPP(RT-PPP)service,namely the Trimble Center Point RTX.Then the post-mission PPP(PM-PPP)coordinates were calculated by using Multi-GNSS data and the Multi-GNSS Experiment(MGEX)precise products.The kinematic RT-PPP and PM-PPP results showed that the PPP coordinates were consistent with the relative solution at centimetre and decimetre level in horizontal and height components,respectively.This study implies that PPP technique is a powerful tool for highly accurate positioning in both real-time and post-mission modes,even for dynamic applications in harsh environments.

On ionosphere-delay processing methods for single-frequency precise-point positioning

In single-frequency precise-point positioning of a satellite,ionosphere delay is one of the most important factors impacting the accuracy. Because of the instability of the ionosphere and uncertainty of its physical properties, the positioning accuracy is seriously limited when using a precision-limited model for correction. In order to reduce the error, we propose to introduce some ionosphere parameter for real-time ionosphere-delay estimation by applying various mapping functions. Through calculation with data from the IGS（ International GPS Service） tracking station and comparison among results of using several different models and mapping functions, the feasibility and effectiveness of the new method are verified.

Modeling and Prediction of Inter-System Bias for GPS/BDS-2/BDS-3 Combined Precision Point Positioning

The combination of Precision Point Positioning(PPP)with Multi-Global Navigation Satellite System(MultiGNSS),called MGPPP,can improve the positioning precision and shorten the convergence time more effectively than the combination of PPP with only the BeiDou Navigation Satellite System(BDS).However,the Inter-System Bias(ISB)measurement of Multi-GNSS,including the time system offset,the coordinate system difference,and the inter-system hardware delay bias,must be considered for Multi-GNSS data fusion processing.The detected ISB can be well modeled and predicted by using a quadratic model(QM),an autoregressive integrated moving average model(ARIMA),as well as the sliding window strategy(SW).In this study,the experimental results indicate that there is no apparent difference in the ISB between BDS-2 and BDS-3 observations if B1I/B3I signals are used.However,an obvious difference in ISB can be found between BDS-2 and BDS-3 observations if B1I/B3I and B1C/B2a signals are used.Meanwhile,the precision of the Predicted ISB(PISB)on the next day of all stations is about 0.1−0.6 ns.Besides,to effectively utilize the PISB,a new strategy for predicting the PISB for MGPPP is proposed.In the proposed strategy,the PISB is used by adding two virtual observation equations,and an adaptive factor is adopted to balance the contribution of the Observed ISB(OISB)and the PISB to the final estimations of ISB.To validate the effectiveness of the proposed method,some experimental schemes are designed and tested under different satellite availability conditions.The results indicate that in open sky environment,the selective utilization of the PISB achieves almost the same positioning precision of MGPPP as the direct utilization of the PISB,but the convergence time of MGPPP is reduced by 7.1%at most in the north(N),east(E),and up(U)components.In the blocked sky environment,the selective utilization of the PISB contributes to more significant improvement of the positioning precision and convergence time than that in the open sky environment.Compared with the direct utilization of the PISB,the selective utilization of the PISB improves the positioning precision and convergence time by 6.7%and 12.7%at most in the N,E,and U components,respectively.

AN EXISTENCE THEOREM OF POSITIVE SOLUTIONS FOR ELASTIC BEAM EQUATION WITH BOTH FIXED END-POINTS

By using the degree theory on cone an existence theorem of positive solution for a class of fourth-order two-point BVP's is obtained. This class of BVP's usually describes the deformation of the elastic beam with both fixed end-points.